Leonardo Jardim's men were seven points adrift of their local rivals heading into the weekend, but closed the gap to four ahead of Benfica's trip to Arouca on Sunday.
Islam Slimani got Sporting off the mark inside the opening two minutes, sending a looping header over helpless goalkeeper Adriano Facchini and into the back of the net.
The men from the Portuguese capital had to wait until second-half stoppage time to double their advantage - Heldon tapping home his first goal in a Sporting shirt to make sure of victory.
At the other end of the table, the battle for top-flight survival took an interesting turn as the division's bottom two clubs both triumphed.
Belenenses were 3-1 winners over Vitoria Guimaraes, lifting themselves out of the relegation play-off position in a match that saw both sides reduced to 10 men.
Rafael Crivellaro opened the scoring for Guimaraes in the second minute, before Chris Malonga was given his marching orders for a second bookable offence.
Belenenses took full advantage of the extra man and moved into the lead through as Deyverson found the net and Fredy converted a penalty.
Fredy then rounded off the victory deep into stoppage-time, despite his side having Deyverson sent off five minutes earlier.
Olhanense, meanwhile, climbed to within two points of Pacos de Ferreira, who play on Monday, with a 2-1 win at Rio Ave.
The league's basement club came from a goal down to claim all three points, but saw Jean-Christophe Coubronne dismissed for a second yellow card six minutes from time.
Elsewhere, Nacional strengthened their grip on a UEFA Europa League berth with a 2-0 win over 10-man Maritimo.
The result lifts them six points clear of sixth-placed Braga, who face Porto on Sunday.
